Daniel Ballesteros-Chávez
Asystent / Assistant
Wydział Matematyki Stosowanej / Dep. Applied Mathematics
Politechnika Śląska / Silesian University of Technology
email: daniel.ballesteros-chavez@polsl.pl
github: http://github.com/ennaniux

My research is on elliptic partial differential equations of fully nonlinear type that appear in geometric problems, for instance, prescribed curvature. A classical problem of this type is the Minkowski problem which is strongly related to the Monge-Ampère equation. I am also interested in the geometry of hypersurfaces in both Riemannian and semi-Riemannian manifolds. These equations are usually represented as symmetric functions on the eigenvalues of the second fundamental form of the hypersurface with respect to the induced metric. Then we can study the properties of the prescription function to ensure the existence of such a hypersurface.